Recovering a sum of two squares decomposition

We present an algorithm that recovers a decomposition of an integer N   as sum of two squares from an approximation to one of the summands. It is based on Coppersmith's linearization technique which, applied directly to this problem, requires an approximation error smaller than N1/6N1/6. Our algorithm performs a two-round linearization and allows approximation errors up to N1/4N1/4.